Problem: Simplify the following expression: $\sqrt{32} - \sqrt{8}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{32} - \sqrt{8}$ $= \sqrt{16 \cdot 2} - \sqrt{4 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{2} - \sqrt{4} \cdot \sqrt{2}$ $= 4\sqrt{2} - 2\sqrt{2}$ Finally, simplify by combining the terms. $= ( 4 - 2 )\sqrt{2} = 2\sqrt{2}$